# Math Help - Suppose we have a right triangle with integer sides

1. ## Suppose we have a right triangle with integer sides

Suppose we have a right triangle with integer sides (in some unit of measure). Prove
(a) One of the legs has a length divisible by 3.
(b) One of the three sides has length divisible by 5.

2. Originally Posted by NikoBellic
Suppose we have a right triangle with integer sides (in some unit of measure). Prove
(a) One of the legs has a length divisible by 3.
We want to show either $m^2-n^2$ or $2mn$ is divisible by $3$.

WLOG if $m\equiv0\bmod{3}$ then we're done since then $2mn\equiv0\bmod{3}$.

So assume $m$ and $n$ are both not divisible by $3$.

But then by flt we get that $m^2\equiv1\bmod{3}$ and $n^2\equiv1\bmod{3}$, so $m^2-n^2\equiv0\bmod{3}$.